Solve the system of equations.

Question

2x + 6y = -18
x = 5y - 1
A. (5.25, 1.25)
B. (-6, -1)
C. (4, 1)
D. (-7.25, -1.25)

Answer 1

To solve the system of equations, we can substitute the second equation into the first equation:

2(5y - 1) + 6y = -18
10y - 2 + 6y = -18
16y - 2 = -18
16y = -16
y = -1

Now, substitute y = -1 back into the second equation to solve for x:

x = 5(-1) - 1
x = -5 - 1
x = -6

Therefore, the solution to the system of equations is x = -6 and y = -1, which corresponds to answer choice B. (-6, -1)

Answer 2

Solve the system of equations.
3x + y = 2
7x - 4y = 30
A. (2, -2)
B. (-2, 8)
C. (2, -4)
D. (1/2, 1/2)

Answer 3

To solve this system of equations, we can use the method of substitution. First, solve one of the equations for one variable and then substitute it into the other equation.

From the first equation:
3x + y = 2
y = 2 - 3x

Now, substitute y = 2 - 3x into the second equation:
7x - 4(2 - 3x) = 30
7x - 8 + 12x = 30
19x - 8 = 30
19x = 38
x = 2

Now, substitute x = 2 back into y = 2 - 3x:
y = 2 - 3(2)
y = 2 - 6
y = -4

Therefore, the solution to the system of equations is x = 2 and y = -4, which corresponds to answer choice C. (2, -4)

Answer 4

Solve the system of equations.
-4x + 6y = 38
x - 5y = -20
A. (-5, 3)
B. (35, -3)
C. (-35, -3)
D. (5, 3)

Answer 5

To solve this system of equations, we can use the method of substitution.

From the second equation, we can express x in terms of y:

x = 5y - 20

Now, substitute x = 5y - 20 into the first equation:

-4(5y - 20) + 6y = 38
-20y + 80 + 6y = 38
-14y = -42
y = 3

Now, substitute y = 3 back into x = 5y - 20:

x = 5(3) - 20
x = 15 - 20
x = -5

Therefore, the solution to the system of equations is x = -5 and y = 3, which corresponds to answer choice A. (-5, 3).

Answer 6

How many solution(s) does this system of equations have?
-5x + y = -18
10x - 2y = 36
A. one
B. two
C. infinite
D. none

Answer 7

To determine how many solutions the system of equations has, we can re-arrange the equations in slope-intercept form (y = mx + b). The system of equations is:

1. -5x + y = -18
2. 10x - 2y = 36

First, isolate y in equation 1:
y = 5x - 18

Then, isolate y in equation 2:
-2y = -10x + 36
y = 5x - 18

When the equations are put in this form, it can be observed that the two equations represent the same line, indicating that the system of equations has infinite solutions.

Therefore, the system of equations has infinite solutions, which corresponds to answer choice C. infinite.